derivative of x/(x+10)

解

\frac{d}{d x} (\frac{x}{x + 10})

\frac{10}{( x + 10 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x}{x + 10})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} ( x + 10 ) - \frac{d}{d x} ( x + 10 ) x}{( x + 10 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x + 10) = 1

= \frac{1 \cdot ( x + 10 ) - 1 \cdot x}{( x + 10 ) ^{2}}

1 \cdot (x + 10) - 1 \cdot x = 10

= \frac{10}{( x + 10 ) ^{2}}